In estimating the distance from Langanes to Svalbarda we are confronted with the difficulty that we do not know where the latter place can have been. I am content, however, to admit that in this case a dægr of twelve hours seems to be indicated. Four times twenty-four hours would penetrate too far into the Arctic regions to be at all probable, while Jan Mayen seems best to fulfil the conditions of a spot to the north of Langanes, situated in the Polar Sea. From the point of Langanes to the southern extremity of Jan Mayen is about 296 miles, or ‘tylfts’ of 74 miles, the route in summer would at this point normally be clear of ice, and altogether it seems probable that Jan Mayen rather than Spitzbergen, as sometimes suggested (840 miles away), is the place described as Svalbarda. The last distance recorded is from Kolbein’s Island (Mevenklint) to the uninhabited coast of Greenland lying to the north. The position of Mevenklint is in lat. 67° 10′ N., long. 18° 30′ W., and the nearest point on the Greenland coast would be about lat. 69° 40′ N., long. 22° 48′ W. The distance would therefore be 177·45 nautical miles, and so it is evident that it could not be covered by a voyage of twelve hours. In twenty-four hours, however, under exceptionally favourable conditions, the whole distance could be traversed, and in any case in that period of time a ship would be likely to have got as close to the land as the ice would permit. It is not likely that this particular voyage, which is not included in all the texts of Landnáma, was sufficiently often accomplished to enable a fair average to be taken; the allusion is more probably to a special case within the knowledge of the authors, which would in all likelihood have taken place on an exceptionally favourable opportunity. Now the conclusions to which we are forced by the consideration of all these distances recorded in Landnáma are as follows: 1. Only two out of the five voyages are at all compatible with a ‘dægr sigling’ of twelve hours. 2. These two appear to be very accurately recorded, which raises a presumption in favour of the correctness of the other data. In the voyage from Stad to C. Horn we have exactly seven ‘tylfts’ of 74·9 miles to cover in seven dægra, in that from Langanes to Svalbarda (if Jan Mayen is meant) four ‘tylfts’ of seventy-four miles each in four dægra. 3. Either the remaining three are hopelessly inaccurate, or a ‘dægr sigling’ in these cases means twenty-four hours. 4. If they are inaccurate, it is a most remarkable coincidence that they can all be made accurate by adopting the basis of twenty-four hours. Thus, taking the average of seventy-five miles in twelve hours at which we had previously arrived: The distance from Stad to C. Horn would take 6·9 or practically seven days of twelve hours (given as seven dægra). If the alternative Horn be taken the voyage would occupy 7·1 days. From Snæfellsnes to Hvarf would be 4·1 days of twenty-four hours (given as four dægra).